Random Hamiltonians with arbitrary point interactions in one dimension

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2021
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Elsevier
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We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we prove the following dichotomy: Either every realization of the random operator has purely absolutely continuous spectrum or spectral and exponential dynamical localization hold. In particular, we establish Anderson localization for Schrödinger operators with Bernoulli-type random singular potential and singular density.

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Damanik, David, Fillman, Jake, Helman, Mark, et al.. "Random Hamiltonians with arbitrary point interactions in one dimension." Journal of Differential Equations, 282, (2021) Elsevier: 104-126. https://doi.org/10.1016/j.jde.2021.01.044.

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